Adding bathroom in large loft style attic. Vent pipe needed?

I have a three story building that currently has a toliet on the 1st and 2nd stories. There is a large attic that I'm going to add a bathroom to.

Both toliets on the 1st and second story are hooked up to the same 4" poopie stack, and I plan to ti the 3rd story tolit into the poopie stack also.

My question is about what I have to do, and how to do it.

I am ok with cutting the cast iron stack, adding a 45 degree 4" booted T-pipe off the main stack, and add the flange for the added toliet in the position where I want the toliet.

Is there anything else that I have to do with the drain for the toliet? i.e. do I need to do anything with vents, etc. to prevent water from flying out of the toliets on the 1st or 2nd floor or anything?

Unfortunately, you cannot do what you are planning on doing. Unless, the second floor toilet is vented separately from the stack, which it won't be.
You will have to run a separate drain line from the third floor toilet into the basement. Or, at least below the second floor toilet. But, really you need a plumber to come and look because we cannot see how the plumbing is run.

In your drawing, the large pipe rising from the second floor towards the attic is presently the vent for the toilets on 1st and 2nd floor. If you turn that pipe into a soil pipe, by putting a toilet on the 3rd floor, that pipe can no longer serve as a vent. Vent pipes from the first and second floor must rise separately and connect back to that large pipe 6" above the highest fixture on the 3rd floor.

How the first floor toilet is connected to the stack is important to the discussion, since it would normally have an offset fitting with the vent as part of it. The second floor would not have the same fitting, although it could look similar outwardly. If so, then you would have to provide a vent for the second floor toilet, not easily done, and disconnect the vent connection from the second floor and reattach it at the same relative point on the third floor. You are not looking at a DIY job, and even an experienced plumber might be challenged depending on the situation.

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As long as you are dumping waste into a pipe, it's a waste stack, and not usable as a vent.

You can tee off as many times as you like, as long as you are adding a vent each time,
Those vents can tie together at six inches above the flood level of the fixtures served.
And then that vent stack can go through the roof on it's own, or tie in above the highest fixture in the home on the top floor.

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I am sure your drawings are very illustrative to you, but to us we have to depend on your descriptions and so far I have not seen anything that tells me HOW the second floor toilet is currently vented. How that is done would determine what has to be done to install a third floor bathroom.